I can generally understand most of the lingo used by ATC and pilots, or I can google it, but something I haven't been able to grasp, mainly because google turns up mainly technical information which is over my head.

When a controller gives an altimeter number for an airport, for example "Kennedy altimeter 3011", to what is that referring? I gather it has something to do with barometric pressure, but beyond that I don't get it.

That's indicating the pressure, in inches of mercury. The pilot will set that barometric pressure in their airplane so that their altimeter reads properly in that area.

As planes can travel great distances, they will travel through areas of varying pressure. This difference in pressure will affect the altitude readout of the altimeter, which won't be accurate unless the correct pressure correction is applied. This readout ("Kennedy Altimeter 30.11") ensures that when pilots approach a runway that may be 200ft above sea level, their altimeter indicates properly, 200ft. This is critical when visibility is poor.

When a plane ascends above 18,000 ft (FL 180) they must set their altimeter to 29.92 inches of mercury. That way all aircraft above that altitude are using the same standard setting on their altimeters so they can keep proper vertical spacing. That is why, when listening to center frequencies working the high sectors, you don't usually hear them calling out altimeter settings.

Kristen, a discrepancy in the barometric setting between an airport's weather station and an airplane's altimeter will cause the altimeter to be off by 100 feet for every tenth of an inch in mercury, or 1,000 feet for every inch.

Sometimes, as did happen to me last week, a controller will call attention to the barometric pressure as a gentle reminder to a pilot to check that their altitude agrees with the intended flightpath. A few seconds into the attached clip the controller repeats the Omaha barometric pressure to me. I declared that I had "Information November" in my initial contact with Omaha Approach, which is code for: "I have the latest weather report from Omaha", so there was no need for him to tell me the current weather. However, I stated in our conversation that I intended to avoid entering Omaha airspace (which has a floor of 2,500 feet in the outer perimeter), and according to his radar screen I hadn't started my decent yet, so he wanted to remind me that I was about to enter the airspace. Stating the local altimeter is a very polite way to say, "check your altitude."